˜v2/2 = 3.8 mm Hg 15 mm Hg 3.8 mm Hg •Fig. 17.2 Inanarrowsection(B)ofatube,thelinearvelocity(v)andhencethedynamiccomponentofpressure(ρv2/2)aregreaterthaninthewidesections(AandC),ofthesametube.Ifthetotalenergyisvirtuallyconstantthroughoutthetube(i.e.,iftheenergylossbecauseofviscosityisnegligible),thelateralpressureinthenarrowsectionislowerthanthelateralpressureinthewidesectionsofthetube(seetheheightsofthecolumnoffluidabovecompartmentsA,B,andCeach,whichreflectpressure).
the energy loss from viscosity is negligible (i.e., this fluid is an “ideal fluid”). The effect of velocity on the dynamic component (Pdyn) can be estimated as follows:
Equation 17.2 where ρ is the density of the fluid (grams per cubic centimeters) and v is velocity (centimeters per second). Assume that the fluid has a density of 1 g/cm3. In section A in
Fig. 17.2 , the lateral pressure is 100 mm Hg; note that 1 mm Hg equals 1330 dynes/cm2. According to
Eq. 17.2, P dyn = 5000 dynes/cm2, or 3.8 mm Hg. In the narrow section B of the tube, where the velocity is twice as high, Pdyn = 20,000 dynes/ cm2, or 15 mm Hg. Thus the lateral pressure in section B is 15 mm Hg lower than the total pressure, whereas the lateral pressures in sections A and C are only 3.8 mm Hg lower. In most arterial locations, the dynamic component is a negligible fraction of the total pressure. However, at sites of an arterial constriction or obstruction, the high flow velocity is associated with large kinetic energy, and the dynamic pressure component may therefore increase significantly. Hence, the pressure would be reduced, and perfusion of distal segments would be correspondingly decreased. This example helps explain how pressure changes in a vessel that is narrowed by atherosclerosis or spasm of the blood vessel •Fig. 17.3 Laminar and Turbulent Flow. A, Whenflowislaminar,allelementsofthefluidmoveinstreamlinesthatareparalleltotheaxisofthetube;thefluiddoesnotmoveinaradialorcircumferentialdirection.Thelayeroffluidincontactwiththewallismotionless;thefluidthatmovesalongthecentralaxisofthetubehasthemaximalvelocity.B, Inturbulentflow,theelementsofthefluidmoveirregularlyinaxial,radial,andcircumferentialdirections.Vorticesfrequentlydevelop.
wall: that is, in narrowed sections of a tube, the dynamic component increases significantly because the flow velocity is associated with large kinetic energy.
The most fundamental law that governs the flow of fluids through cylindrical tubes was derived empirically by the French physiologist Jean Léonard Marie Poiseuille in the 1840s. He was interested primarily in the physical determinants of blood flow, but he replaced blood with simpler liquids in his measurements of flow through glass capillary tubes. His work was so precise and important that his observations have been designated Poiseuille’s law.
Poiseuille’s law applies to the steady (i.e., nonpulsatile) laminar flow of newtonian fluids through rigid cylindrical tubes. A newtonian fluid is one whose viscosity remains constant, and laminar flow is the type of motion in which the fluid moves as a series of individual layers, with each layer moving at a velocity different from that of its neighboring layers (